Dam construction



Demy 28 1926. 1,612,50

L. R. JORGENSEN DAM CONSTRUCTION v Filed Feb. 4. 1924 Patented @een 2S, lilith LABS R. JORGENSEN, OF BERKELEY, CALIFORNIA., SSIGNOR, BY MESNE SSGN- IENTS, TO CONSTANT ANGLE ARCH DAM COMIPANY, OF SAN FRANCESCO, CALI- FOB/NIA, A CORFORATION OF CALIFORNIA. I

DAM CONSTRUCTIDN.

rlhis invention relates to a dam structure, and particularly to concrete dams of the arch type.

An arch dam can be designed either with the Lip-stream and down-stream face struck from the same center at all elevations or from the same centers at various horizontal elevations.

TWhen the Water load acts on an arch dam the arch deforms` due to the strain oeveloped in the material. When the crown of the arch is forced in a down-stream direction b v the water pressurey principally and also by Chrinkagre dne to setting, drop in temperature and rib shortenine. bending stresses are set up in the arch besides the axial compression. rl`hese bendingr stresses tor-an arch having concentric up and downstream faces are a maximum at the abutments.` l

In order to malte an economical arch dam design or structure, it is therefore necessary to deviate from the nsual method oi dam construction having concentric circular faces and to space the faces uneqnally from one another, atleast 'tor a part ot the dam body, sov that at 1points ot maximum bending moments the distance lzetween the faces or, in other Words, the dam thickness, W'll be zgreatest.

The object., therefore, of the present invention is to so construct a dam of the characier described that it is equally salie and economical in all its parts, which practically means that each section should be so proportioned that the maximum allowable liber stress at the crown shall be, equal to that at the abutments or as nearly so as possible, and that the shear and cantilever stresses towardsl the bottom and at the bottom shall be held closel;T within safe limits.

The method ot reinforcing the darny and the detail construction thereof are more fully described in the appended speeilica tion andv drawings, in Wh1ch- Fig. l is a plan View of an arch darn across a canyon where the snbtended angle is kept as near constant and as near 120 as po=sibleg this View also showing the contour lines 1from the bottom et the dam to the crest thereof, the contour lines being indim cated by the numerals D l), 20(), l5-4:5, 70-70, 90-90 and 10G-'MXL G--O representing the contour lines at the crest of the darn and 10G-100 representing the contour lines of the river or bottom of the dam.

Fig. 2 is a central vertical cross-section taken on line 2-2, Fig. l.

Fig. 3 is a horizontal plan section taken on line 3 3, Fig. 2

Fig'. 4 is a horizontal plan cross-section taken on line fl-AL Fig. 2.

Fig. 5 is a horizontal plan cross-section taken on line 5-5, Fig. 2.

An arch dam et the character here illus trated can he designed either with the npstream or down-stream faces strnclrom the same center at all elevations or from the same centers at various horizontal eleva tions.

"When the Water load acts on an arch dam ot this character the arch deforme, due to the strain developed in the material; that is, when the crown ot-the arch is forced in a down-stream direction b v the Water pressure, and also by shrinkage due to setting, drop in temperature and rib shortening, bending stresses are set up in the arch besides the axial compression. Applying the ordinary' bendincr orrnul as for loaded arches to any particular arch dam, discloses the 'tact that the bending moment is a mairimnm at the abutment-s and gradually (liminishesto zero at the points of contratlexnre, which points are located a distance trom each abutment very close to 21% ot the length of the middle are.

A maximum nnit compression is therefore introduced in the material on the down stream side at the. alontments, and a minkimum nnit compression on the upstream side of the clam at the abutments; this minimum unit compression is often actual tension..v

From the abntments towards 'thelf two points of contraflexure this difference inI unit loading is gradually disappearing; fand does disappear entirely at the points of contra'tlexure, where the average compression is much less than the maximum at the abutments j lt can, therefore, be readilj,T seen 'that iter economyls sake, extra material should be added only Where thestresses are concentrated, and that the thickness added should be in proportion this concentration. As the increase ot' unit stress alcove the average along the down-stream :tace ceases a distancev of 2l% of the length of the arc from each abutment, there would be no object in adding material beyond this point. In' fact, it is proper 4to stop the addition ot' material at a distance of approximately 18% of the length of the arc out from the abutments. At these points the addition should be zero,

l increasing approximately uniformly to a maximum at the abutments. The amount to be added (the thickness) is dictated by the maximum allowable stress which is assumed before starting on the"design.

Near and at the bottom of an arch dam. arch action is very incomplete and the load is therefore taken up by cantilever and shear action, The cantilever here supports the 'greatest load in the middle between the abutments where the height of the dam is the greatest, and the deflection of the cantileverin a down-stream direction the greatest with the reservoir full. Hence, greater thickness is often required inthe middle of the dam than at the abutments near the bottom. f

@n the other hand, dam sites may be found where archV action even close to the bottpm would be considerable and cantilever action notso great. This would require greater thickness at the abutments than in the middle, due to the predomination of bending in a horizontal plane over that in a vertical plane. The combination of cantilever and arch action which constitutes the actual resultant load carrier will on such site, therefore require the lower part of the dam to have concentric up-a'nd-down-stream faces in order to have the material stressed to a point where the factor of safety for shear and for compression is as near equal as it can be made.

lt is for this reason that dam sites can be found where it would be most economical to start the dam with concentric upanddowncrease the thickness at and towards the abutments at higher elevations in order to take care of the increased horizontal bendinf; moment at these higher elevations. This thickening at and towards the abutments should preferably be taken care of on the down-stream side in order to keep the middle radius small and the subtended angle as large as possible. Some material may, however, be added on the upstream side, as

shown in my former Patent No. 1.087,662 at the point f, as shown in' Fig. 2. The additional material thus applied should have a maximum thickness at the ahutments and should then diminish to Zero towards the point oinv coutra-tlexure. Forl instance, as illustrated at A and B in Fig. 4.

Other dam sites may sometimes b e found` as mentioned above where calculation would show that it wonldbc most economical to shape the bottom of thc dam so that it would be thicker in the middle than at the abutcase be kept subtantially circular in a horizontal plane or as nearly so possible. Towards higher elevations the two faces might be required to be concentric in a .certain zone. Above this zone the dam sections might have to be thickened between Jthe abutments and points of contra-flexure With a maximum addition at the abutment tapering to nothing toward the points of contralexure, as previously referred to in Fig. 4..

and in the upper zone towards the crest of the dam the up-and-*down-stream faces may again be required to be-made concentric for vthe whole horizontal arch as illustrated in Fig. The material in this Zone can not be highly stressed for practical reasons.

' Different dam sites may require-different combinations.

would have to be calculated at a sutlicient Y number of elevations to admit of designing In each case the moments and their resultinlgr stresses 1n the material tive to one an ther in order to obtain an.

architect-urally ractical structure. ln a V- shaped canyon the rule also holds that the angle subtcnded by the arch should be as A near at all elevations as possible. stream JFaces at thc bottom and gradually in- At most sites it will not be found possible to keep the subtended angle as large as 120 towards the lower elevations, but the rule is nevertheless to attempt to do so by changing the length of the radii corresponding to the shaped elements in the middle zone being the' same in any horizontal plane to a location just past the points of contra-flexure, from where the thickness gradually increases to a maximum at the abutments, and the radial thickness of the arch-shaped elements in the iii imrizontal plane to a location just past the points of 'contra-flexure, from Jqvhere `the thickness gradually increases to a maximum at the abutmen'ts for a' distance of about 15 to per cent of the length of the arch, and the radial thickness of the arch-shaped elements in the bottom "zone having a maximuni thickness in the middle and a minimum or towards the abutments.y

3. An arch dam divided into an upper, a

mirldle and a lower zone and comprising superpcsed integral arch-shaped elements of various thicknesses in diiiierent zones and at Various elevations, the radial thickness of the arch-shaped elements being the same in any. horizontal plane in the upper zone near u the crest, the radial thickness of the archshaioed elements in the middle zone being the same in any horizontal lane to a loca tion just past the points o contra-flexure, from where the tluckness is gradually increased to a maximum at the abutments, and the radial thickness of the arch-shaped elements in the bottom zone being the same 'in any horizontal plane.

4l. An arch dam divided into an upper, a

'middle and a lower zone and comprising superposecl integral arch-shaped elements of varying radn, the center of curvature of such elements being out of vertical align- .ment and the radial thickness of the archshaped elements being thesame in any horizontal plane in the upper zone near the crest, the radial thickness of the arch-shaped elements in the middle zone being the same in any horizontal plane to a location just past the points of contraflexure, from where the `thickness is gradually increased to a maximum at the abutments, said gradualincrease in thickness taking place for a dis-V tance of about 15 to 20 per cent of the length of the arch, and the radial thickness of the arch-shaped elements in the lower zone being the same in any horizontal plane.

5. An arch dam divided into an upper, a middle and a lower zone and comprisinsuperposed integral arch-shaped elements o various thicknesses in different zones, the radial thickness of the arch-shaped elements being the same in any horizontal plane in thenpper zone, near the crest, and in the middle zone the thickness of the arch dcreasing gradually from the abutments for a distance of l5 to 2O per cent of the length of the arch towards theY points of contralexure.

6. 'An arch dam divided into an upper,-

a middle and a lower zone and comprismg superposed integral arch-shaped elements of various radii, the center of curvature of such elements being 'out of vertical alignment and the radial thickness of lthe archshaped elements being the same in any horizontal plane in the u per zone, near the crest', and in the midd e zone the thickness of the arch decreasing gradually from the abutments for a distance of 15 to 20 per cent of the length of the arch towards the points' of. contra-flexure.

LABS R. J ORGEN SEN. 

